A LEAR 55 FLC EXPERIENCED AN ENG FAILURE AT FL410; DIVERTED TO NEARBY ARPT.

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WE WERE AT CRUISE ALT (FL410) FOR APPROX 15-20 MINS. OUR TOTAL TIME INTO THE FLT FROM SRQ TO AGC WAS 1 HR 10 MINS. OUR R ENG ROLLED BACK AND BECAME UNRESPONSIVE TO THROTTLE MOVEMENT. WE DID NOT HAVE ANY ANNUNCIATOR OR CIRCUIT BREAKERS POPPED. THE ENG WAS DEVELOPING SOME PWR; SO WASN'T SECURED. WE ASKED ZTL FOR LOWER AND ALSO NEAREST ARPT (AUGUSTA) AND WX. WE WERE IN AN AREA OF TSTMS (BELOW US). WE WERE EVENTUALLY TURNED OVER TO AUGUSTA APCH/TWR AND RECEIVED THE WORST HANDLING I HAVE EVER HAD. AFTER WE WERE AT 4000 FT; WE WERE TOLD RWY LIGHTS OUT ON LONGEST RWY (RWY 17/34). WE ASKED SEVERAL TIMES FOR VECTORS FOR STRAIGHT-IN TO RWY 26. ATC INSISTED ON SETTING US UP ON A BASE AND EVENTUALLY PAINTED OUT AN ARPT. WE ASKED IF IT WAS AGS AND WERE TOLD 'NO;' THEN 'OH; YES; THAT'S IT.' AGAIN WE ASKED FOR A STRAIGHT-IN AND WE SET UP FOR THE CLOSED RWY WITH EQUIP ON IT. OUR ALT WAS 1600 FT PER ATC. WE WERE IN TURB AND BEING UNFAMILIAR WITH OBSTACLES IN AREA. GOT SET UP FOR RWY 26. ALTHOUGH WE WERE A LITTLE FAST; WE TOUCHED DOWN AND BEGAN HYDROPLANING. WE DRIFTED TO R OF RWY AND R MAIN WENT OFF. WE GOT IT BACK ON RWY AND EXITED THE END INTO THE OVERRUN AREA. WE TOOK OUT SOME RWY LIGHTS AND BLEW A COUPLE TIRES. WE NEVER WOULD HAVE ATTEMPTED A LNDG ON THE 6000 FT RWY HAD WE BEEN INFORMED PRIOR TO LNDG THAT A VERY HVY RAIN SHOWER HAD JUST PASSED THROUGH AND RWY WAS WET WITH STANDING WATER. APPARENTLY; THE TWR DIDN'T THINK THAT IMPORTANT ENOUGH. THE FIREMAN TOLD US OF THE WX. THIS WAS MY FIRST ENG ROLLBACK/LOSS IN 20 YRS OF FLYING -- COUPLED WITH POOR WX; POOR ATC HANDLING AND FATIGUE (I WAS ON FOR 10 HS; MY PARTNER ON FOR 12 HRS). I FELT OVERWHELMED AT THE END OF FLT.